“I don’t attack people on their weaknesses. That usually doesn’t get the job done,” Karl Rove once said. “Voters already perceive weaknesses. You’ve got to go after the other guy’s strengths.”

Mitt Romney is trying to turn the tables on President Obama. (Steven Senne/AP)

A recent USA Today/Gallup Poll found Obama has an 18-point lead with female voters in key swing states. New Washington Post-ABC News polling found a 19-point gap with women nationwide; both men and women trusted Obama to handle “women’s issues” by a 19-point margin. Democrats have been hammering on what they call a Republican “war on women.”

Romney, this week, came up with a counterpoint: 92 percent of the jobs lost in the recession belonged to women. It’s Obama who has waged the true anti-women war, by taking away their livelihoods with his misguided economic policies.

There have been multiple conference calls. Female allies are out with statements declaring that Obama’s policies have harmed women. At a rally in Delaware Tuesday night, Romney was surrounded by female supporters.

“I think what he’s doing is smart,” said Republican strategist Sara Fagen. “It’s such a part of the narrative right now that he has really no choice to address it.”

Asked to expand on how the president’s policies hurt women in particular, his staff couldn’t answer. Asked if Romney supported the Lily Ledbetter Fair Pay Restoration Act, which makes it easier for workers’ to sue over gender-based pay disparities, they again were unsure.

Two hours later, a spokeswoman clarified that Romney “supports pay equity and is not looking to change current law” — after Ledbetter herself sent out a statement attacking the Republican candidate.

Democrats, meanwhile, appear gleeful that Romney has not only engaged on the issue but adopted the “war on women” phrase. “So, can we keep this back and forth over whose policies are better for women going please,” tweeted Democratic National Committee spokesman Brad Woodhouse.

It’s true that the connection between contraceptive access and political polls is murky, as former Bush White House speechwriter Michael Gerson pointed out earlier this week. In the USA Today/Gallup poll, Rick Santorum — who once said birth control harms women — outperformed Romney by a few points. Most respondents didn’t know Romney’s position on contraception policy.

Now that the primary is effectively over, Romney can focus on introducing himself to women voters. But simply trying to turn around a Democratic attack line with a questionable factoid isn’t going to solve his problem.